Introduction
Creation Functions
Creation of Structures FunctionField(R) : Rng -> FldFunRat FunctionField(R, r) : Rng, RngIntElt -> FldFunRat FieldOfFractions(P) : RngUPol -> FldFunRat
Names AssignNames(~F, s) : FldFunRat, [ MonStgElt ]) -> Name(F, i) : FldFunRat, RngIntElt -> FldFunRatElt
Creation of Elements F ! [a, b] : FldFunRat, RngUPolElt, RngUPolElt -> FldFunRatElt F ! a : FldFunRat, FldElt -> FldFunRatElt K . i : FldFunRat, RngIntElt -> FldFunRatElt Example FldFunRat_FunctionField (H37E1)
Structure Operations
Related Structures IntegerRing(F) : FldFunRat -> RngPol BaseRing(F) : FldFunRat -> Rng Rank(F) : FldFunRat -> RngIntElt ValuationRing(F) : FldFunRat -> RngVal ValuationRing(F, f) : FldFunRat, RngUPolElt -> RngVal
Invariants
Ring Predicates and Booleans
Homomorphisms hom< P -> S | f, y1, ..., yn > : FldFunRat, Rng -> Map Example FldFunRat_Homomorphism (H37E2)
Element Operations
Arithmetic
Equality and Membership
Numerator, Denominator and Degree Numerator(f) : FldFunRatElt -> RngElt Denominator(f) : FldFunRatElt -> RngElt Degree(f) : FldFunRatElt -> RngIntElt TotalDegree(f) : FldFunRatElt -> RngIntElt WeightedDegree(f) : FldFunRatElt -> RngIntElt
Predicates on Ring Elements
Evaluation Evaluate(f, r) : FldFunRatUElt, RngElt -> FldFunRatUElt Evaluate(f, v, r) : FldFunRatMElt, RngIntElt, RngElt -> FldFunRatMElt
Derivative Derivative(f) : FldFunRatUElt -> FldFunRatUElt Derivative(f, k) : FldFunRatUElt, RngIntElt -> FldFunRatUElt Derivative(f, v) : FldFunRatMElt, RngIntElt -> FldFunRatMElt Derivative(f, v, k) : FldFunRatMElt, RngIntElt, RngIntElt -> FldFunRatMElt
Partial Fraction Decomposition PartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ] SquarefreePartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ] Example FldFunRat_PartialFractionDecomposition (H37E3) [Next][Prev] [Right] [____] [Up] [Index] [Root]
